\makeatletter
\pgfplotsset{
    groupplot xlabel/.initial={},
    every groupplot x label/.style={
        /pgfplots/every axis x label,
        anchor=south,
        yshift=2ex
    },
    groupplot ylabel/.initial={},
    every groupplot y label/.style={
        /pgfplots/every axis y label,
        anchor=south,
        yshift=2ex
    },
    execute at end groupplot/.code={%
      \node [/pgfplots/every groupplot x label] at ($(group c1r1.north
west)!0.5!(group c1r\pgfplots@group@columns.south west)$)
{\pgfkeysvalueof{/pgfplots/groupplot xlabel}};
      \node [/pgfplots/every groupplot y label] at ($(group c1r1.north
west)!0.5!(group c1r\pgfplots@group@rows.south west)$)
{\pgfkeysvalueof{/pgfplots/groupplot ylabel}};
    }
}

\def\endpgfplots@environment@groupplot{%
    \endpgfplots@environment@opt%
    \pgfkeys{/pgfplots/execute at end groupplot}%
    \endgroup%
}
\makeatother